Four friend went to the movie. Each ticket cot $8 and each peron brought popcorn and a oda for $5 dollar. How much did they pend in all? Show two way to write the expreion or equation and olve

The inverse of the logarithmic function f(x) = [tex]\log_{e}x[/tex] is [tex]e^{x}[/tex].

In the given question, we have to find the inverse of the logarithmic function f(x) = [tex]\log_{e}x[/tex].

The given function is f(x) = [tex]\log_{e}x[/tex].

The features of logarithms will simply follow from our understanding of exponents if the logarithm is viewed as the inverse of the exponential function.

Now let, y = [tex]\log_{e}x[/tex]

Now x = log y

Then, y = [tex]e^{x}[/tex]

So, f(x) = [tex]e^{x}[/tex]

As a result, [tex]e^{x}[/tex] is the logarithmic function's inverse, where f(x) = [tex]\log_{e}x[/tex].

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The complete question is:

What is the inverse of the logarithmic function f(x) = [tex]\log_{e}x[/tex]?

The density is 12.5 grams per cubic centimeter and 80 grams per cubic centimeter.

What is the density?

Density is a measure of how much mass is contained in a given volume. It is defined as the ratio of mass to volume and is typically measured in units of grams per cubic centimeter (g/cm^3) or kilograms per liter (kg/L).

The mass is 500 grams and the volume is 40 cubic centimeters, therefore the density is:

density = mass / volume = 500 grams / 40 cubic centimeters = 12.5 grams per cubic centimeter

The mass is 125 grams and the volume is v cubic centimeters. To find the value of v, you can use the equation:

density = mass / volume = 125 grams / v cubic centimeters

so v = mass / density = 125 grams / 12.5 grams per cubic centimeter = 10 cubic centimeters

The volume is 1.4 cubic centimeters and the density is 80 grams per cubic centimeter. To find the mass you can use the equation:

mass = density x volume = 80 grams per cubic centimeter x 1.4 cubic centimeters = 112 grams

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The value of X will be 96 [tex]ft^{2}[/tex].

From the question, we can conclude that the shape is Triangle.

What is Triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Hence we will use the formula of the area of a triangle.

Area of Triangle = bh/2.

In question, it's given that our Base is 12 ft and our Height is 16 ft.

Area = (12*16)/2

Area = 96 [tex]ft^{2}[/tex]

Therefore our value of area i.e. X will be 96 [tex]ft^{2}[/tex].

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The 1/10 gradient means  6 degrees is the angle of 1 in 10 slopes.

The gradient is the inclination of a line. The gradient is often referred to as the slope (m) of the line. The gradient or slope of a line inclined at an angle θ is equal to the tangent of the angle θ.

In geometry, 1 in 10 means for every ten units of horizontal distance crosses there is 1 unit of vertical drop or rise. The angle of tan is used to measure this value of the slope. Let x be the angle to be used for tan.

[tex]tanx=\frac{horixontal distance}{vertical distance}[/tex]

[tex]tanx= \frac{1}{10}=0.1[/tex]

[tex]x=tan^{-1}(0.1)\\x=5.71'[/tex]

By rounding to the nearest digit, the degree value will be 6.

Hence, 6 degrees is the angle of 1 in 10 slopes.

Hence, the 1/10 gradient means  6 degrees is the angle of 1 in 10 slopes.

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Answer:

(3x + 1)(x + 7)

Step-by-step explanation:

3x² + 22x + 7 =

3x² must factor into 3x and x.

= (3x +    )(x +     )

7 factors into 7 and 1. We can place 7 and 1, or 1 and 7.

= (3x + 7)(x + 1)

or

= (3x + 1)(x + 7)

Now we multiply both possibilities out to see which one produces the middle term 22x that we need.

= (3x + 7)(x + 1) = 3x² + 10x + 7     No what we need

or

= (3x + 1)(x + 7) = 3x² + 2x + 7      Exactly what we need

Answer: (3x + 1)(x + 7)

You have to distribute it. To do this, multiply x^2 to (7x^2-5x-5) and do the same to 9 times (7x^2-5x-5). Add like variables. The attached image is your answer.

I hope this was able to help you :D

Answer: The right side of the first equation is 78, and the right side of the second equation is -72. Both equations are correct.

In the first equation, 2(3b+6) = 78, if we solve for b we get b= 11.

In the second equation, -2(6c-3) = -72, if we solve for c we get c = 6.5.

Step-by-step explanation:

No, 1/3 and 2/7 are not the equivalent fractions.

In mathematics, equivalent fractions are those with the same denominator and differing numerators. For instance, because 2/4 and 3/6 are both equal to 1, they are both comparable fractions. Part of a whole is a fraction. Identical portions of the whole are represented by equivalent fractions.

Every fraction has an equivalent fraction, which can be found by multiplying the numerator and denominator by the same integer. In spite of their visual differences, equivalent fractions are those that indicate the same value. For instance, if you take a piece of cake, divide it into two equal pieces, then eat one of them, you will have consumed half of the cake.

let us consider,

1/3 = 2/7

0.33 = 0.29

so, it is not equals.

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Correct Question:

Are 1/3 and 2/7 equivalent fractions?.

Answer:

$700

Step-by-step explanation:

1. We see the original price is $1,000.

2. Change 30% to a decimal

3. 30/100=0.30

4. Multiply the original cost of the item(mattress) by the percentage.

5. 0.3×1,000=300

6. $300 is the amount discounted.

7. For final price with discount: Take its original price($1,000) and subtract the discount from the original price

8. $1,000-$300=$700

Answer:

$300

Step-by-step explanation:

The assertion that both zeros of the quadratic polynomial x² - 2kx +2 in magnitude but opposite in sign then value of k is 1/2 is false.

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The sum of the roots of a quadratic function is given as follows:

S = -b/a.

The equation in this problem is given as follows:

x² - 2kx +2

Hence the parameters are:

a = 1, b = -2k.

If the roots are equal in magnitude but the opposite sign, the sum of the roots is of:

0.

Hence:

-b/a = 0.

b = 0.

Meaning that the value of k is obtained as follows:

-2k = 0.

k = 0.

And the statement is false.

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An angle has a length of 166.7°. The extra degree at 166.7 is 13.3

Given,

The measure of an angle is 166.7°.

The supplement of 166.7 degrees is 180 - 166.7  = 13.3

Therefore the answer is 13.3°

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Answer:50.00

Step-by-step explanation:

First you need to find what 15% of 39.62 is 5.94 or 6 so you would add 6 to 39.62 and get 34.62 then you round it all and get 35 and it is closer to 50 than 40.

Yes, 3 * ( 5 - 2 ) = ( 3 * 5 ) - ( 3 * 2 ) is an example of distributive law.

The distributive property is also known as the distributive law of multiplication over addition and subtraction. The name itself implies that the operation involves dividing or distributing something. The distributive law applies to addition and subtraction. The formula for the distributive property is expressed as:

Over addition : a( b + c ) = ab + ac

and subtraction : a( b - c) = ab - ac

Example: Solve the expression 7(20 + 3)

Multiplication of 7(20) and 7(3) is done before addition. This leads to 7(20) + 7(3) = 140 + 21 = 161.We have, an expression 3×(5 - 2) =(3 × 5 ) - (3× 2 ).

Consider the left hand side, 3×(5 - 2)

=> 3× 5 - 3× 2 = 15 - 6 = 9

Now, the right hand side, (3 × 5 ) - (3× 2 ) => 15 - 6 = 9 = LHS

Hence, it is an example of distributive law.

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Complete question:

Is 3 * ( 5 - 2 ) = ( 3 * 5 ) - ( 3 * 2 ) an example of distributive law *?.

The amount he earned last week in commission is $994.

The commission he earned in 2011 is $51,688

The commission earned is a fraction of the total sales of stocks.

Commission earned = amount of sales x percentage commission

14% x $7,100

= 14/100 x $7,100

= 0.14 x $7,100

= $994

Amount she earned in commission in a year = number of weeks in a year x commission earned per week

= $994 x 52 = $51,688

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Yes , the graphing calculator can be used as a scientific calculator.

As given in the question,

Scientific calculator can not be used as a graphing calculator.

But graphing calculator can be used as a scientific calculator.

Therefore, yes the graphing calculator can be used in place of scientific calculator.

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Answer:

[tex]8^{9}[/tex]

Step-by-step explanation:

[tex]8^{5}[/tex] x [tex]8^{4}[/tex]

In expanded form this would be

8·8·8·8·8·8·8·8·8

The product of power principle tells us that when we are multiplying powers with the same bases, we add the exponents.

Answer:

see attachement

Step-by-step explanation:

To find the first term can be calculated an = a1 + d(n - 1).

The difference between every two successive terms in a sequence is the same; this is known as an arithmetic progression (AP). It is possible to obtain a formula for the nth term of the AP using this kind of development. A good example of an arithmetic progression (AP) is the series 2, 6, 10, 14,..., which follows a pattern in which each number is created by adding 4 to the previous term. The nth term in this series equals 4n-2. You may get the terms of the series by changing the nth term to n=1,2,3,... i.e.,

first term = 4n-2 = 4 when n = 1 (1)

-2 = 4-2=2

Second term for n = 2 is 4n-2 = 4. (2)

-2 = 8-2=6

When n is 3, the third term is 4n-2 (3)

-2 = 12-2=10

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Therefore , the solution of the given problem of surface area comes out to be 160 peoples can be fit in that region.

Its surface area is a good indicator of how much space it takes up overall. When estimating the surface area of a three-dimensional shape, the entire environment is taken into consideration. Its surface area determines how big something is overall. The sum of the faces on any and all six of a cuboid's rectangular sides yields the amount of water contained within.

Here,

Given : one person occupies 360 square inches

is 2.5 square foot.

So,

The given dimension of region are :

length = 20 feet and width 20 feet.

Thus,

=> Area = 20*20

=> Area = 400 square foot.

So , number of people in that area will be :

=> 400/2.5

=> 160 peoples.

Therefore , the solution of the given problem of surface area comes out to be 160 peoples can be fit in that region.

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The product of 2x2x2 is 8.

A product is the outcome of multiplication in mathematics, or an expression that specifies the factors (numbers or variables) to be multiplied. For instance, the sum of 6 and 5 is 30. (the result of multiplication).

So 2x2x2 = 4x2= 8

Integers, natural numbers, fractions, real numbers, complex numbers, and quaternions are examples of typical special instances where it is possible to define the product of two numbers or the multiplication of two numbers.

In linear algebra, there are numerous different types of products. Some of them have names that sound confusingly close but have very distinct meanings (outside product, external product), while others have names that sound completely different but basically imply the same thing (outer product, tensor product, Kronecker product). These are briefly discussed in the sections that follow.

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The credit utilisation ratio to the nearest percentage is found as 17%.

Steps:

For the stated question:

Balance = $180 + $230 = $410.

credit limits = $1500 + $1000 = $2500.

Credit utilisation ratio = Balance / credit limits

Credit utilisation ratio = 410 / 2500 * 100 = 16.4%

Thus, the credit utilisation ratio to the nearest percentage is found as 17%.

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The Number which is more than 99 is 100.

Number:

Numbers are mathematical objects used for counting, measuring, and labeling. The original example is the natural numbers 1, 2, 3, 4, etc. [1] Numbers can be linguistically represented by numerals. More generally, individual numbers can be represented by symbols called digits. For example, "5" is the number representing the number five. Since only a relatively small number of symbols can be remembered, basic numbers are usually organized into number systems, which are systematic ways of representing each number. The most common number system is the Hindu-Arabic number system, which can represent any number using combinations of 10 basic numeral symbols called digits.

Greater than Number:

Greater than or equal to in mathematics is an inequality used to compare two or more numbers, quantities, or values. Used when one quantity or number is greater than or greater than the second or remaining quantity or number. This indicates that one value is greater than or greater than or greater than the other. The above symbol is ">". This is also called greater than.  For example, Bella has a red pencil that is 5 cm long and a blue pencil that is 3 cm long.

According to the Question:

1 more than 99 is:

adding 1 +99 = 100.

Therefore,

1 more than 99 is 100.

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When the coin is tossed and then dice is rolled, the possible outcomes are 12.

For the stated question.

Sample space for tossing coin. { H, T}.

Sample space for rolling dice. { 1, 2, 3, 4, 5, 6 }

Then,

Total sample = { H1, H2, H3,H4, H5, H6, T1, T2, T3, T4, T5, T6}

Thus, the total possible outcomes for tossing coin and rolling dice is 12.

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Answer:

the answer is option A

Step-by-step explanation:

Distance between two points

/XY/ = √((X2-X1)²+(Y2-Y1)²)

Therefore

/XY/= √((7-(-5)²+(15-4)²)

Answer:

First a farl we should know,

Distance (d) = √(x2-x1)^2+ (y2-y1)^2

x(-5,4) = (x1, y1)

y(7,15) = (x2, y2)

Now,

Distance (d) = √(x2-x1) + (y2-y1)

Ans = √(7-5)^2 + (15-4)^2

Answred by : - ||Ziddiboy||

Answer:

Answer in attached photo.

Step-by-step explanation:

Steps are in the attached photo, this question is testing on the concept of Similar Triangles.

Formula:

[tex]\frac{Shorter \ Length \ of \ line \ segment \ A}{Longer \ Length \ of \ line \ segment \ A} = \frac{Shorter \ Length \ of \ line \ segment \ B}{Longer \ Length \ of \ line \ segment \ B}[/tex]

Raul's distance from Main street decreases in the interval,

0 ≤ t ≤ 0.75. And Raul walks 6 miles to get to school.

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}.

Given:

Raul crosses Main Street when he walks home from school.

The graph of the function d(t)=4I(t-0.75)I shows Raul's distance, in miles, from Main Street after t hours.

The domain of the function is 0 ≤ x ≤ 1.5.

The graph shows his entire trip.

From the graph;

Raul's distance from Main street decreases in the interval,

0 ≤ t ≤ 0.75.

And to get to school,

Raul walks,

distance = (distance when t = 1.5) - (distance when t = 0)

Distance = (4 x 0.75) - (4 x -0.75)

Distance = 3 -(-3)

Raul walks = 6 miles.

Therefore, Raul walks 6 miles to get to school.

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The complete question is given on the attached image,

The next operation that should be done when evaluating this expression is -12

The rules that specify the order in which we should perform several operations to solve an expression are known as the order of operations. Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are the sequence in which the operations are performed (from left to right).

The next operation that should be done when evaluating this expression is

9-12+6/-3+3(-3)

Addition or Subtraction (from left to right)

9-12=-5

Multiplication or Division (from left to right)

6 /-3 = -2

-5 + -2+3(-3) = -12

The next operation that should be done when evaluating this expression is -12

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Answer:34

Step-by-step explanation:

ad divided by 79=34

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.